Sigma Fields: Definition and Examples

This lecture introduces the concept of sigma fields, which are collections of subsets of a fundamental set, such as the outcomes of an experiment. The instructor explains the three axioms that a sigma field must satisfy and provides examples using a di-roll experiment and continuous intervals. The lecture also covers the concept of sigma fields generated by a collection of events, highlighting the importance of these structures in probability theory. The instructor discusses the Borrel Sigma field on the interval zero to one and extends the concept to the real line and higher dimensions, emphasizing the role of sigma fields in defining measurable sets for probability calculations.